: The OED cites several instances of "no skin off my nose" and various other places, such as "bugle" for nose, "off me" and "off my ass." It did not mention "off my back." It means, of course, "It's all the same to me," or "I don't care." SS

Coal miners have to crawl when the roof is low. There was a scene in "Coal Miner's Daughter" (the movie about singer Loretta Lynn). She asks her father why he didn't wear his knee pads so his knees wouldn't get skinned up. Mr. Lynn said if he wears knee pads, then his back scrapes on the roof -- literally taking skin off his back. So he wouldn't wear his knee pads sometimes to give his back a rest.